Minimum Leadfield-Variance Beamformer with Voxel-Wise Orthonormal Leadfield

In biomagnetic inverse problem, the estimated signal source distribution is practically required to provide with sharpness, smoothness, bias-free, high resolution, etc. Some of the requirements conflict each other. We propose the newly developed biomagnetic signal source estimation method, the minimum leadfield-variance beamformer (MLVB) with the voxel-wise orthonormal leadfield (VWOL) for compromising the requirements. This method consists of two techniques: VWOL) leadfields are reconstructed for orthonormalization both in signal source space and in MEG data space; and MLVB) the minimum variance beamformer (MVB) is modified with the covariance matrix based on forward model. Simulation was performed for evaluating MLVB with VWOL and for comparing with the weighted minimum L2 norm (WMN) solution and the standardized low resolution brain electromagnetic tomography (sLORETA) solution. MLVB with VWOL solution was shaper and smoother than WMN solution, and moreover was bias-free. However, MLVB with VWOL dose not produce feasible solutions. Although MLVB with VWOL solution is quite similar to sLORETA solution, MLVB with VWO is apt to slightly emphasize the resolution of the estimated signal source distribution comparing with sLORETA solution. On the other hand, VWOL itself, a modified leadfields, can be used with other biomagnetic inverse techniques. Keywords—biomagnetic inverse problem, leadfield, magnetoencephalography, minimum norm estimation, minimum variance beamformer, standardized low resolution brain electromagnetic tomography.